which diverges and the divergence corresponds to the translational symmetry of the extra internal vertex produced after gluing as in the original Ponzano-Regge state-sum model [1]}, [2]}.
In the state-sum model, this divergence can be eliminated by fixing the spin (thus edge length, say \(\ell _{l}\) ,) of one internal edge incident to this internal vertex.
In a similar spirit,
(REF ) can be viewed as the gauge-fixing version of (REF ) which fixes one spinor \(z_2\)  in the bulk. Another way of gauge fixing is to gauge fix (the norm of) the inner product \(|[z_1|z_2\rangle |\)  of the two spinors \(z_1,z_2\)  used to define the face amplitude \({\mathcal {A}}_{f^*}^{e_1}\)  and \({\mathcal {A}}_{f^*}^{e_2}\) , which encodes the angle information of the triangle dual to the node that \(z_1,z_2\)  lives on (see Section REF  below). This can be seen by rewriting \(\delta _{\mathrm {SU}(2)}(\mathbb {I})\)  in terms of \(|[z_1|z_2\rangle |\)  as
\(\begin{split}\delta _{\mathrm {SU}(2)}(\mathbb {I})=&\int _{\mathrm {SU}(2)}\mathrm {d}g\int \mathrm {d}\mu (z_1)\mathrm {d}\mu (z_2) \,(\langle z_1|z_1 \rangle -1)(\langle z_2|z_2 \rangle -1) e^{\langle z_1|g|z_1 \rangle } e^{\langle z_2|g|z_2\rangle } \\=&\int \mathrm {d}\mu (z_1)\mathrm {d}\mu (z_2) \, (\langle z_1|z_1 \rangle -1)(\langle z_2|z_2 \rangle -1)e^{|[z_1|z_2\rangle |^2}\,.\end{split}\) 
